The present invention relates generally to the operation of measurement instruments. More specifically, the invention relates to measurement instruments consisting of analog-to-digital converters (ADCs) which are used to sample or digitize an analog signal, converting the analog signal to an array of values whose magnitude represents the voltage of the signal and the location in the array represents when the signal was sampled. Furthermore, the present invention relates to digitizing systems, which consist of multiple, interleaved ADCs.
Systems used to digitize analog signals utilize analog-to-digital converters that sample an analog signal at a time specified by a sample clock that is fed to the ADC. On prescribed rising and/or falling edges of this sample clock, the ADC samples the analog signal providing a digital value at its output. This digital value is typically stored in a memory of some sort for later use.
Waveform digitizing systems such as digital oscilloscopes are used by scientists and engineers to build ever faster electronic equipment. Because the speed of electronic equipment continues to increase, there is an ever-increasing demand for faster waveform digitizing systems. Recently, the speed demands placed on waveform digitizing systems have outpaced the physical capabilities of analog-to-digital converters. In other words, analog-to-digital converters which presently exist cannot sample signals fast enough to meet the demands of the electronics industry and the scientific community.
In order to overcome this physical limitation and make waveform-digitizing systems which sample signals at a higher rate, a technique called interleaving is used. Interleaving involves the usage of multiple ADCs in a waveform digitizing system. These ADCs are used in a manner in which all ADCs sample at the same rate, but they sample the signal at different times. For example, a waveform digitizing system utilizing two ADCs could sample a signal at an effective sample rate of 1 Gsample/second (1 Gs) if each ADC sampled the signal at 500 Ms, and each of these ADCs took every other sample of the signal. At the end of such a waveform acquisition, the resulting array of data points would contain data where half of the data was generated from one ADC and the other half from the other. More specifically, every other point in the resulting acquired signal would have been acquired by one of the ADCs while the remaining points were acquired by the other. This method of interleaving ADCs has been used with great success. Some digital sampling oscilloscopes utilize up to 16 interleaved ADCs in the acquisition of waveforms.
While bandwidth and sample rates of waveform digitizer systems are perhaps the most important qualities, accuracy of the system is almost equally important. In other words, the waveform digitizing system is expected to produce a digital representation of the sampled analog waveform with a high degree of accuracy. Said differently, the digitizing system is expected to faithfully reproduce an image of the analog signal being digitized. In systems utilizing a single ADC to digitize a waveform, the problem of faithful reproduction of the analog signal reduce to the solution of engineering problems in the design of the digitizer system involving front-end non-linearity and noise, ADC integral and differential non-linearity, sample clock accuracy and stability etc. In interleaved systems, these problems are exacerbated by the use of multiple digitizers.
First, the signal path to each digitizer must have identical characteristics. Any time delay, attenuation or gain applied differently in the path to each digitizer will result in noticeable degradation of the quality of the acquired signal. The same must be said for the sample clock delivery to the digitizers. Any variation in the timing from digitizer to digitizer will reduce the signal quality. Furthermore, each digitizer or ADC in an interleaved system will have characteristics that may vary from the other digitizers, the most important characteristic being frequency response. Differing frequency response manifests itself as a mismatching gain and time delay of the signal at various frequencies. Differences in frequency response are most likely at higher frequencies where different pole locations in the transfer function of the digitizers result in poor matching and therefore poor signal quality. As mentioned previously, high bandwidth is another feature desired of digitizing systems, and high bandwidth means that high frequency signals or signals with components at high frequencies are being digitized. This means that matching digitizer frequency response characteristics is a particular problem in high bandwidth systems that are used to digitize high frequency signals.
The current state of technology deals with these problems in several ways. In the design of a digital oscilloscope or other waveform digitizing system, good engineering practice is applied to ensure that the sample clock does not jitter and is delivered accurately to each digitizer. Furthermore, the paths to each digitizer are carefully designed and routed to provide as good signal path matching as practically possible. Finally, demands are placed on the designers of ADC chips to meet stringent frequency response specifications.
Additionally, ADCs are sometimes built with controls provided to precisely adjust the offset, gain, and sample clock delay to the ADC. Some systems dynamically measure and adjust the offset, gain and delay characteristics of the individual digitizers in the interleaved system using internal calibration signals and hardware controls. Even with the provision of these controls, it is still impossible to adjust for gain and delay characteristics of the digitizers that vary with frequency.
In summary, waveform-digitizing systems are incapable of meeting the increasing demands of the electronics industry using single digitizing elements. To address this, digitizing systems are sometimes designed utilizing multiple, interleaved digitizing elements which sample the same signal at different points in time. Interleaving creates problems in that mismatching digitizer characteristics degrade the quality of the digitized signal. Although many techniques are used to improve the signal quality, it is currently not possible to adjust the digitizers so that the frequency response between digitizers matches.
It would therefore be beneficial to provide an improved waveform digitizing system that overcomes these problems of the prior art.
It is therefore an object of the invention to provide an improved method and apparatus for digitizing high speed waveforms.
A further object of the invention is to provide an improved method and apparatus for digitizing high speed waveforms employing interleaved ADCs.
Another object of the invention is to provide an improved method and apparatus for digitizing high speed waveforms employing interleaved ADCs and compensating for differences in frequency response and other characteristics of the interleaved ADCs.
A still further object of the invention is to provide an improved method and apparatus for digitizing a high speed waveform employing a system of interleaved ADCs that provides complete recovery of the applied high speed waveform as if the system consisted of a plurality of interleaved digitizers with perfectly ideal frequency response characteristics.
Still other objects and advantages of the invention will in part be obvious and will in part be apparent from the specification and the drawings.
Generally speaking, the invention provides a method and apparatus for recovering a waveform whose acquisition and digitization has been contaminated by non-ideal digitizer frequency response characteristics. The present invention also deals with problems incurred by waveform acquisition systems utilizing multiple interleaved digitizers whose frequency response characteristics are non-ideal and mismatching.
FIG. 1 depicts such a digitizing apparatus, including a signal being applied to a waveform digitizing system employing multiple interleaved digitizing elements. This system generates an acquired signal, which is corrected in the waveform recovery system to generate a recovered signal. This invention focuses primarily on the functioning of the waveform recovery system.
FIG. 2 shows an example of a signal that might be applied to a digitizing system. It shows a single pulse from a train of pulses. This is an ideal signal in many ways in that it contains no noise. Moreover, it represents a good example signal because it represents a signal commonly digitized and a signal consisting of many frequency components. FIG. 3 shows what the acquired signal might look like when acquired by a system of interleaved digitizing elements, each having a different frequency response from the others. FIG. 4 shows the same acquired signal as in as well as showing which digitizer in the system acquired each point. This figure uses four individual digitizing elements as an example, with the understanding that the present method is applicable to any number of digitizers.
In summary, FIGS. 3 and 4 show an acquisition by a waveform digitizing system employing multiple interleaved digitizing elements, which does not represent a faithful reproduction of the signal applied in FIG. 2. It has been mathematically determined by the inventor that if the frequency response characteristics of each digitizer are known, then the actual signal that the digitizing system is attempting to sample may be recovered from the acquired data.
The present invention operates by first storing the measured frequency response characteristics for each digitizer. These characteristics can be measured at the factory or dynamically. They can he determined by the digitization of pure-sinusoidal signals at various frequencies whose amplitude and phase is known or by determining the step or impulse response from a step or pulse whose characteristics are well known. By examining the resulting magnitude and phase of the signal acquired by the digitizers at various frequencies, the frequency response of the digitizers can be measured. Once the frequency response of each digitizer is known an array of matrices are generated by the system. The generation of and principle behind these arrays are described subsequently, and comprise key elements of the invention. These generated arrays are then stored in memory. When a waveform is digitized, the acquired waveform is passed to a waveform recovery system, constructed in accordance with the invention, for processing. This system may be embodied in a digital signal processing system, a computer, or an embedded system considered as a back-end to the data acquisition system.
The system of the invention takes each digitized waveform, and calculates the Discrete Fourier Transform (DFT) of the waveform, thus determining the frequency components of the signal acquired. The frequency component values for the acquisition shown in FIG. 3 are shown in FIGS. 5 and 6 on the traces labeled acquired signal. These figures show the magnitude and phase values that make up a frequency component. From these components, an array of vectors is generated. This array of vectors has the same number of elements as the array of matrices previously stored as a result of the digitizer frequency response measurement. Additionally, each vector contains the same number of rows as the number of rows and columns in the matrices mentioned previously. Each vector is pre-multiplied by its corresponding matrix, thus generating an array of new vectors. These vectors are in turn used to generate a set of frequency components that represent those of the actual signal applied to the digitizer system. The invention generates the frequency component values shown in FIGS. 5 and 6 on the traces labeled applied signal. The inverse DFT is used to generate the recovered signal. The recovered signal is the signal which would have been acquired if the waveform digitizing system were made up of individual interleaved digitizers whose frequency response were unity at all frequencies.
The invention accordingly comprises the several steps and the relation of one or more of such steps with respect to each of the others, and the apparatus embodying features of construction, combination(s) of elements and arrangement of parts that are adapted to effect such steps, all as exemplified in the following detailed disclosure, and the scope of the invention will be indicated in the claims.